Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 99.9%

Time: 7.2s

Alternatives: 3

Speedup: N/A×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ e^{\left(x \cdot y\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(((x * y) * y));
end

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{\left(x \cdot y\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(((x * y) * y));
end

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 1 + \mathsf{expm1}\left(x \cdot {y}^{2}\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (expm1 (* x (pow y 2.0)))))

C

double code(double x, double y) {
	return 1.0 + expm1((x * pow(y, 2.0)));
}

Java

public static double code(double x, double y) {
	return 1.0 + Math.expm1((x * Math.pow(y, 2.0)));
}

Python

def code(x, y):
	return 1.0 + math.expm1((x * math.pow(y, 2.0)))

Julia

function code(x, y)
	return Float64(1.0 + expm1(Float64(x * (y ^ 2.0))))
end

Wolfram

code[x_, y_] := N[(1.0 + N[(Exp[N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. log1p-expm1-u 100.0%

      \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(x \cdot \left(y \cdot y\right)\right)\right)}} \]

   2. log1p-undefine 100.0%

      \[\leadsto e^{\color{blue}{\log \left(1 + \mathsf{expm1}\left(x \cdot \left(y \cdot y\right)\right)\right)}} \]

   3. add-exp-log 100.0%

      \[\leadsto \color{blue}{1 + \mathsf{expm1}\left(x \cdot \left(y \cdot y\right)\right)} \]

   4. pow2 100.0%

      \[\leadsto 1 + \mathsf{expm1}\left(x \cdot \color{blue}{{y}^{2}}\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{1 + \mathsf{expm1}\left(x \cdot {y}^{2}\right)} \]
7. Add Preprocessing

Alternative 2: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{x \cdot \left(y \cdot y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* x (* y y))))

C

double code(double x, double y) {
	return exp((x * (y * y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((x * (y * y)))
end function

Java

public static double code(double x, double y) {
	return Math.exp((x * (y * y)));
}

Python

def code(x, y):
	return math.exp((x * (y * y)))

Julia

function code(x, y)
	return exp(Float64(x * Float64(y * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = exp((x * (y * y)));
end

Wolfram

code[x_, y_] := N[Exp[N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 50.1% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-*l* 100.0%

      \[\leadsto e^{\color{blue}{x \cdot \left(y \cdot y\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot \left(y \cdot y\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 46.4%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))